Expanding reamers of the type which are here discussed are known. They have a basic element, as well as an annular portion on whose outer face there is defined at least one geometrically defined cutting edge. The radial position of the at least one cutting edge is adjusted by means of an adjusting device comprising an adjusting screw. For this purpose, an adjusting element of the adjusting device, having a conical or spherical outer face, is moved with the aid of the adjusting screw in the direction of the center axis of the expanding reamer, so that it widens the annular portion to a greater or lesser extent. It has been shown that the adjusting element of the adjusting device is subjected to high wear and that an exact positioning of the at least one cutting edge often fails, because the position of the adjusting element is dependent on the position of the thread in the basic element in which the adjusting screw engages. The thread is frequently not exactly concentric to the center axis of the expanding reamer, so that the radius of the at least one cutting edge is not precisely adjustable. If the expanding reamer has a plurality of geometrically defined cutting edges, it is in many cases not possible to adjust these such that they lie exactly on the same orbit.